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Description Logics

Description Logics

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Description Logics

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  1. Description Logics

  2. Outline • Knowledge Representation • Ontology Language • Description Logics • Application

  3. Knowledge Representation • Object: find implicit meaning in explicit knowledge • Concentration: since 1970, research of this field falls into two division—logic-based and cognitive method (network structure or problem solving) • Logic in Knowledge Representation: 1 Formalized semantics (reasoning function to symbol) 2 Operators and interpretation (semantics of logic expression) 3 Functional explanation of other methods (semantic web, frame-based) 4 In structure-based KR (OWL), reasoning service is related with computing complexity

  4. Ontology Language • Classification by structure: Frame-based: FLogic, OKBC, KM Description logic-based: OWL First order logic-based: Cycl, KIF frame: definition and restriction of expressiveness, formalism and characteristics • Logic in Ontology: 1 Ontology designing: contradiction and hierarchies in concepts 2 Ontology building: consistency, inclusion of instances

  5. Description Logics • Components • Research • Example: SHIQ

  6. Description Logics Component • Constructors: existential restriction value restriction number restriction • Terminological axioms: definition & restriction • Assertion Formalism: attributes of instance • Subsumption Algorithm • Instance Algorithm • Consistency Algorithm: check consistency in terminological axioms and assertions

  7. Research in Description Logics • Key Problem in the field: Tradeoff between expressiveness and reasoning complexity of Description Logics

  8. Research Stages • Phase 1 (1980-1990) System implementation implying structural subsumption algorithm, but it’s not complete for expressive Description Logics. Computing complexity of most DLs’ reasoning service exceeds polynomial. Example: KL-ONE, K-REP, BACK, LOOM, CLASSIC

  9. Research Stages • Phase 2 (1990-1995) 1 Tableau-based algorithms are used for reasoning services in DLs, especially for propositionally closed DLs (DLs with all of Boolean constructors) and it is complete for expressive DLs. 2 A thorough examination into various DLs. 3 Subsumption and satisfiability are ascribed to consistency in propositionally closed DLs, thus consistency algorithm can solve three reasoning problems in DLs. KRIS and CRACK show optimized implementation of such algorithm is acceptable, though its worst-case complexity is not polynomial. 4 Description Logics is relevant to modal logic.

  10. Research Stages • Phase 3 (1995-2000) Research of reasoning service in very expressive DLs falls into two concentrations: tableau-based methods and transfering to modal logic. Highly optimized system like FaCT, RACE, DLP show tableau-based algorithms obtain preferable performance even for expressive DLs with large knowledge base.

  11. Research Stages • Phase 4 (2001-) Industrial strength Description Logics System and tableau –based algorithms research Application: Semantic Web, Knowledge Representation and Integration in Bioinformatics

  12. Facilities in Description Logics • A navigator for the complexity of description logics by Evgeny Zolin.

  13. SHIQ • It is a kind of Description Logics. • Components: value restriction, terminological axioms inverse roles subroles • Extensions: Concrete Domain: real number, integer, strings, built-in predicates(eg, <=, <=13, isPrefixof). Non restricted use of concrete domain will largely affect decidability and complexity of underlying DLs. Nominals: sets of unique instance

  14. SHIQ • Basically, OWL is based on SHIQ, though its underlying DL is more expressive than SHIQ. • OWL has a very restricted ways of using concrete domain. • Reasoning problem in SHIQ is decidable, though its worst-case complexity is EXPTIME.

  15. Application • Selection and combination of language structure matter to reasoning characteristics and complexity. • There are three ways of implementing knowledge representation system: 1 limited language + complete polynomial reasoning algorithms eg, CLASSIC 2 expressive language + incomplete reasoning algorithms eg, BACK, LOOM 3 expressive language + complete reasoning algorithm eg, KRIS

  16. Application: System Composition • Two ways for application + Description Logics 1 Description Logics -- integrated development environment for the system and it interacts loosely with application program 2 Description Logics is the reasoning component of the system, functions like data management is implemented by other techniques. It depends on the application

  17. Application: Knowledge Vagueness • Probabilistic logic Knowledge: probabilistic terminological axioms (information) + probabilistic assertions (credibility) Reasoning for finding subsumption and assertion probability • Fuzzy Logic